Exact Confidence Interval Construction
and Test of Hypothesis for
The Binomial Populations


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Professor Hossein Arsham   


Enter the needed information, and then click the Calculate button.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

Application to the test of hypothesis: Notice that, one may utilize Confidence Interval (CI) for the test of hypothesis purposes. Suppose you wish to test the following general test of hypothesis:

H0: The population parameter is almost equal to a given claimed value,

against the alternative:

Ha: The population parameter is not even close to the claimed value.

The process of carrying the above test of hypothesis at a level of significance using CI is as follow:

  1. Ignore the claimed value in the null hypothesis, for time being.
  2. Construct a 100(1- a)% confidence interval based on the available data.
  3. If the constructed CI does not contain the claimed value, then there is enough evidence to reject the null hypothesis. Otherwise, there is no reason to reject the null hypothesis.



Sample Size (n):
Number-of- Successes (m):
Required Confidence Level (1-a):
The Point Estimate:
The Lower Confidence Limit:
The Upper Confidence Limit:


Confidence Intervals for Finite Population
Population Size (N):
Sample Size (n):
Number-of- Successes (m):
Required Confidence Level (1-a):
The Point Estimate:
The Lower Confidence Limit:
The Upper Confidence Limit:


For Technical Details, Back to:
Statistical Thinking for Decision Making


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Professor Hossein Arsham


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Professor Hossein Arsham   


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